This all comes down to your goals for your game. You need to ask yourself: "why am I considering adding variable damage? What problem does it help fix, or what player experience does it help serve?"
As you note, randomized damage provides roughly the types of gameplay impacts we get from critical hits, so most of the reasons discussed in that Q&A thread can also apply to non-critical damage variation, if you find your critical hits alone aren't fully serving those goals.
A reason to pursue randomized damage ranges beyond just discrete criticals could be verisimilitude: the real world is messy. Even an expert in a skill usually doesn't perform it identically every time. So an element of randomness in the exact damage number can express that, and make the character's actions feel slightly more organically inconsistent, rather than mechanically same-y.
But if your game is about robots or computer programs battling in the digital world, maybe that kind of organicity actually speaks against your game's thematic goals.
One reason to not have randomized damage is if you want to make it easy for the player to predict the outcome several steps into the future, like a tactics game, or one with RPG elements where you want the player to be able to make analytical judgements about which build to use. And where you want this type of min-maxing gameplay to be clearly legible and learnable, not obfuscated behind a layer of superficial variation.
But if you're designing a game for more casual play and don't want players getting sucked into analysis paralysis where they try to min-max every encounter, a little random fuzz can help them resist that temptation.
The more random variation you add, the more inconsistent the gameplay can feel. On the plus side, this can keep the player on their toes, or force them to mix up their play when the random rolls don't always come out the same, increasing variety and combatting stagnant dominant strategies. But too much can make the game feel capricious, like it's "cheating", or de-value player agency, and also make your mechanics harder to learn (especially if you have small percent damage buffs whose effects can get swamped by random noise).
So you need to interrogate what you want out of your game's combat system, what you're getting out of your existing critical mechanics, and whether there's a delta left over that needs to be served by additional variation or other changes to your systems.